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942 lines
38 KiB
PHP
942 lines
38 KiB
PHP
{
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$Id$
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This file is part of the Free Pascal run time library.
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Copyright (c) 1993,97 by Carl-Eric Codere,
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member of the Free Pascal development team
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See the file COPYING.FPC, included in this distribution,
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for details about the copyright.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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**********************************************************************}
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{*************************************************************************}
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{ lowmath.inc }
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{ Ported to FPK-Pascal by Carl Eric Codere }
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{ Terms of use: This source code is freeware. }
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{*************************************************************************}
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{ This inc. implements low-level mathemtical routines for the motorola }
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{ 68000 family of processors. }
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{*************************************************************************}
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{ single floating point routines taken from GCC 2.5.2 Atari compiler }
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{ library source. }
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{ Original credits: }
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{ written by Kai-Uwe Bloem (I5110401@dbstu1.bitnet). }
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{ Based on a 80x86 floating point packet from comp.os.minix, }
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{ written by P.Housel }
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{ Patched by Olaf Flebbe (flebbe@tat.physik.uni-tuebingen.de) }
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{ Revision by michal 05-93 (ntomczak@vm.ucs.ualberta.ca) }
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{*************************************************************************}
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{--------------------------------------------------------------------}
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{ LEFT TO DO: }
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{ o Add support for FPU if present. }
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{ o Verify if single comparison works in all cases. }
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{ o Add support for NANs in SINGLE_CMP }
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{ o Add comp (80-bit) multiplication,addition,substract,division, }
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{ shift. }
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{ o Add stack checking for the routines which use the stack. }
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{ (This will probably have to be done in the code generator). }
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{--------------------------------------------------------------------}
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Procedure Single_Norm;Assembler;
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{--------------------------------------------}
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{ Low-level routine to normalize single e }
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{ IEEE floating point values. Never called }
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{ directly. }
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{ On Exit: }
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{ d0 = result. }
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{ Registers destroyed: d0,d1 }
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{--------------------------------------------}
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Asm
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tst.l d4 { rounding and u.mant == 0 ? }
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bne @normlab1
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tst.b d1
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beq @retzok
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@normlab1:
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clr.b d2 { "sticky byte" }
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@normlab3:
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move.l #$ff000000,d5
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@normlab4:
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tst.w d0 { divide (shift) }
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ble @normlab2 { denormalized number }
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move.l d4,d3
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and.l d5,d3 { or until no bits above 23 }
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beq @normlab5
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@normlab2:
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addq.w #1,d0 { increment exponent }
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lsr.l #1,d4
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or.b d1,d2 { set "sticky" }
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roxr.b #1,d1 { shift into rounding bits }
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bra @normlab4
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@normlab5:
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and.b #1,d2
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or.b d2,d1 { make least sig bit "sticky" }
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asr.l #1,d5 { #0xff800000 -> d5 }
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@normlab6:
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move.l d4,d3 { multiply (shift) until }
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and.l d5,d3 { one in "implied" position }
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bne @normlab7
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subq.w #1,d0 { decrement exponent }
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beq @normlab7 { too small. store as denormalized number }
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add.b d1,d1 { some doubt about this one * }
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addx.l d4,d4
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bra @normlab6
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@normlab7:
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tst.b d1 { check rounding bits }
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bge @normlab9 { round down - no action neccessary }
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neg.b d1
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bvc @normlab8 { round up }
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move.w d4,d1 { tie case - round to even }
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{ dont need rounding bits any more }
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and.w #1,d1 { check if even }
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beq @normlab9 { mantissa is even - no action necessary }
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{ fall through }
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@normlab8:
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clr.w d1 { zero rounding bits }
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add.l #1,d4
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tst.w d0
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bne @normlab10 { renormalize if number was denormalized }
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add.w #1,d0 { correct exponent for denormalized numbers }
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bra @normlab3
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@normlab10:
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move.l d4,d3 { check for rounding overflow }
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asl.l #1,d5 { #0xff000000 -> d5 }
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and.l d5,d3
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bne @normlab4 { go back and renormalize }
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@normlab9:
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tst.l d4 { check if normalization caused an underflow }
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beq @retz
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tst.w d0 { check for exponent overflow or underflow }
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blt @retz
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cmp.w #255,d0
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bge @oflow
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lsl.w #8,d0 { re-position exponent - one bit too high }
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lsl.w #1,d2 { get X bit }
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roxr.w #1,d0 { shift it into sign position }
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swap d0 { map to upper word }
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clr.w d0
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and.l #$7fffff,d4 { top mantissa bits }
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or.l d4,d0 { insert exponent and sign }
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movem.l (sp)+,d2-d5
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rts
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@retz:
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{ handling underflow should be done here... }
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{ by default simply return 0 as retzok... }
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@retzok:
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moveq.l #0,d0
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lsl.w #1,d2
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roxr.l #1,d0 { sign of 0 is the same as of d2 }
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movem.l (sp)+,d2-d5
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rts
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@oflow:
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move.l #$7f800000,d0 { +infinity as proposed by IEEE }
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tst.w d2 { transfer sign }
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bge @ofl_clear { (mjr++) }
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bset #31,d0 { }
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@ofl_clear:
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or.b #2,ccr { set overflow flag. }
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movem.l (sp)+,d2-d5
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rts
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end;
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Procedure Single_AddSub; Assembler;
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{--------------------------------------------}
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{ Low-level routine to add/subtract single }
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{ IEEE floating point values. Never called }
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{ directly. }
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{ On Exit: }
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{ d0 = result -- from normalize routine }
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{ Flags : V set if overflow. }
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{ on underflow d0 = 0 }
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{ Registers destroyed: d0,d1 }
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{--------------------------------------------}
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Asm
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{--------------------------------------------}
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{ On Entry: }
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{ d1-d0 = single values to subtract. }
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{--------------------------------------------}
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XDEF SINGLE_SUB
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eor.l #$80000000,d0 { reverse sign of v }
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{--------------------------------------------}
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{ On Entry: }
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{ d0, d1 = single values to add. }
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{--------------------------------------------}
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XDEF SINGLE_ADD
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movem.l d2-d5,-(sp) { save registers }
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move.l d0,d4 { d4 = d0 = v }
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move.l d1,d5 { d5 = d1 = u }
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move.l #$7fffff,d3
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move.l d5,d0 { d0 = u.exp }
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move.l d5,d2 { d2.h = u.sign }
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swap d0
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move.w d0,d2 { d2 = u.sign }
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and.l d3,d5 { remove exponent from u.mantissa }
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move.l d4,d1 { d1 = v.exp }
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and.l d3,d4 { remove exponent from v.mantissa }
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swap d1
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eor.w d1,d2 { d2 = u.sign ^ v.sign (in bit 15)}
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clr.b d2 { we will use the lowest byte as a flag }
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moveq.l #15,d3
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bclr d3,d1 { kill sign bit u.exp }
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bclr d3,d0 { kill sign bit u.exp }
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btst d3,d2 { same sign for u and v? }
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beq @slabel1
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cmp.l d0,d1 { different signs - maybe x - x ? }
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seq d2 { set 'cancellation' flag }
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@slabel1:
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lsr.w #7,d0 { keep here exponents only }
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lsr.w #7,d1
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{--------------------------------------------------------------------}
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{ Now perform testing of NaN and infinities }
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{--------------------------------------------------------------------}
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moveq.l #-1,d3
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cmp.b d3,d0
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beq @alabel1
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cmp.b d3,d1
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bne @nospec
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bra @alabel2
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{--------------------------------------------------------------------}
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{ u is special. }
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{--------------------------------------------------------------------}
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@alabel1:
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tst.b d2
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bne @retnan { cancellation of specials -> NaN }
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tst.l d5
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bne @retnan { arith with Nan gives always NaN }
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addq.w #4,a0 { here is an infinity }
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cmp.b d3,d1
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bne @alabel3 { skip check for NaN if v not special }
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{--------------------------------------------------------------------}
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{ v is special. }
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{--------------------------------------------------------------------}
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@alabel2:
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tst.l d4
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bne @retnan
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@alabel3:
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move.l (a0),d0
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bra @return
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{--------------------------------------------------------------------}
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{ Return a quiet nan }
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{--------------------------------------------------------------------}
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@retnan:
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moveq.l #-1,d0
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lsr.l #1,d0 { 0x7fffffff -> d0 }
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bra @return
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{ Ok, no inifinty or NaN involved.. }
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@nospec:
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tst.b d2
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beq @alabel4
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moveq.l #0,d0 { x - x hence we always return +0 }
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@return:
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movem.l (sp)+,d2-d5
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rts
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@alabel4:
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moveq.l #23,d3
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bset d3,d5 { restore implied leading "1" }
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tst.w d0 { check for zero exponent - no leading "1" }
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bne @alabel5
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bclr d3,d5 { remove it }
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addq.w #1,d0 { "normalize" exponent }
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@alabel5:
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bset d3,d4 { restore implied leading "1" }
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tst.w d1 { check for zero exponent - no leading "1" }
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bne @alabel6
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bclr d3,d4 { remove it }
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addq.w #1,d1 { "normalize" exponent }
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@alabel6:
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moveq.l #0,d3 { (put initial zero rounding bits in d3) }
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neg.w d1 { d1 = u.exp - v.exp }
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add.w d0,d1
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beq @alabel8 { exponents are equal - no shifting neccessary }
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bgt @alabel7 { not equal but no exchange neccessary }
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exg d4,d5 { exchange u and v }
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sub.w d1,d0 { d0 = u.exp - (u.exp - v.exp) = v.exp }
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neg.w d1
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tst.w d2 { d2.h = u.sign ^ (u.sign ^ v.sign) = v.sign }
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bpl @alabel7
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bchg #31,d2
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@alabel7:
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cmp.w #26,d1 { is u so much bigger that v is not }
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bge @alabel9 { significant ? }
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{--------------------------------------------------------------------}
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{ shift mantissa left two digits, to allow cancellation of }
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{ most significant digit, while gaining an additional digit for }
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{ rounding. }
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{--------------------------------------------------------------------}
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moveq.l #1,d3
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@alabel10:
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add.l d5,d5
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subq.w #1,d0 { decrement exponent }
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subq.w #1,d1 { done shifting altogether ? }
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dbeq d3,@alabel10 { loop if still can shift u.mant more }
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moveq.l #0,d3
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cmp.w #16,d1 { see if fast rotate possible }
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blt @alabel11
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or.w d4,d3 { set rounding bits }
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clr.w d4
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swap d4
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subq.w #8,d1
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subq.w #8,d1
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bra @alabel11
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@alabel12:
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move.b d4,d2
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and.b #1,d2
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or.b d2,d3
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lsr.l #1,d4 { shift v.mant right the rest of the way }
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@alabel11:
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dbra d1,@alabel12 { loop }
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@alabel8:
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tst.w d2 { are the signs equal ? }
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bpl @alabel13 { yes, no negate necessary }
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tst.w d3 { negate rounding bits and v.mant }
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beq @alabel14
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addq.l #1,d4
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@alabel14:
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neg.l d4
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@alabel13:
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add.l d4,d5 { u.mant = u.mant + v.mant }
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bcs @alabel9 { needn not negate }
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tst.w d2 { opposite signs ? }
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bpl @alabel9 { do not need to negate result }
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neg.l d5
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not.l d2 { switch sign }
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@alabel9:
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move.l d5,d4 { move result for normalization }
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clr.l d1
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tst.l d3
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beq @alabel15
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moveq.l #-1,d1
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@alabel15:
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swap d2 { put sign into d2 (exponent is in d0) }
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jmp SINGLE_NORM { leave registers on stack for norm_sf }
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end;
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Procedure Single_Mul;Assembler;
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{--------------------------------------------}
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{ Low-level routine to multiply two single }
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{ IEEE floating point values. Never called }
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{ directly. }
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{ Om Entry: }
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{ d0,d1 = values to multiply }
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{ On Exit: }
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{ d0 = result. }
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{ Registers destroyed: d0,d1 }
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{ stack space used (and restored): 8 bytes. }
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{--------------------------------------------}
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Asm
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XDEF SINGLE_MUL
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movem.l d2-d5,-(sp)
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move.l d0,d4 { d4 = v }
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move.l d1,d5 { d5 = u }
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move.l #$7fffff,d3
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move.l d5,d0 { d0 = u.exp }
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and.l d3,d5 { remove exponent from u.mantissa }
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swap d0
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move.w d0,d2 { d2 = u.sign }
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move.l d4,d1 { d1 = v.exp }
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and.l d3,d4 { remove exponent from v.mantissa }
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swap d1
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eor.w d1,d2 { d2 = u.sign ^ v.sign (in bit 15)}
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moveq.l #15,d3
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bclr d3,d0 { kill sign bit }
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bclr d3,d1 { kill sign bit }
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tst.l d0 { test if one of factors is 0 }
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beq @mlabel1
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tst.l d1
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@mlabel1:
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seq d2 { 'one of factors is 0' flag in the lowest byte }
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lsr.w #7,d0 { keep here exponents only }
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lsr.w #7,d1
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{--------------------------------------------------------------------}
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{ Now perform testing of NaN and infinities }
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{--------------------------------------------------------------------}
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moveq.l #-1,d3
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cmp.b d3,d0
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beq @mlabel2
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cmp.b d3,d1
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bne @mnospec
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bra @mlabel3
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{--------------------------------------------------------------------}
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{ first operand is special }
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{--------------------------------------------------------------------}
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@mlabel2:
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tst.l d5 { is it NaN? }
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bne @mretnan
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@mlabel3:
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tst.b d2 { 0 times special or special times 0 ? }
|
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bne @mretnan { yes -> NaN }
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cmp.b d3,d1 { is the other special ? }
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beq @mlabel4 { maybe it is NaN }
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{--------------------------------------------------------------------}
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{ Return infiny with correct sign }
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{--------------------------------------------------------------------}
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@mretinf:
|
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move.l #$ff000000,d0 { we will return #0xff800000 or #0x7f800000 }
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lsl.w #1,d2
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roxr.l #1,d0 { shift in high bit as given by d2 }
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@mreturn:
|
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movem.l (sp)+,d2-d5
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rts
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{--------------------------------------------------------------------}
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{ v is special. }
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{--------------------------------------------------------------------}
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@mlabel4:
|
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tst.l d4 { is this NaN? }
|
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beq @mretinf { we know that the other is not zero }
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@mretnan:
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moveq.l #-1,d0
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lsr.l #1,d0 { 0x7fffffff -> d0 }
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bra @mreturn
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{--------------------------------------------------------------------}
|
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{ End of NaN and Inf }
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{--------------------------------------------------------------------}
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@mnospec:
|
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tst.b d2 { not needed - but we can waste two instr. }
|
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bne @mretzz { return signed 0 if one of factors is 0 }
|
|
moveq.l #23,d3
|
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bset d3,d5 { restore implied leading "1" }
|
|
subq.w #8,sp { multiplication accumulator }
|
|
tst.w d0 { check for zero exponent - no leading "1" }
|
|
bne @mlabel5
|
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bclr d3,d5 { remove it }
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|
addq.w #1,d0 { "normalize" exponent }
|
|
@mlabel5:
|
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tst.l d5
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beq @mretz { multiplying zero }
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|
|
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moveq.l #23,d3
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bset d3,d4 { restore implied leading "1" }
|
|
tst.w d1 { check for zero exponent - no leading "1" }
|
|
bne @mlabel6
|
|
bclr d3,d4 { remove it }
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|
addq.w #1,d1 { "normalize" exponent }
|
|
@mlabel6:
|
|
tst.l d4
|
|
beq @mretz { multiply by zero }
|
|
|
|
add.w d1,d0 { add exponents, }
|
|
sub.w #BIAS4+16-8,d0 { remove excess bias, acnt for repositioning }
|
|
|
|
clr.l (sp) { initialize 64-bit product to zero }
|
|
clr.l 4(sp)
|
|
{--------------------------------------------------------------------}
|
|
{ see Knuth, Seminumerical Algorithms, section 4.3. algorithm M }
|
|
{--------------------------------------------------------------------}
|
|
move.w d4,d3
|
|
mulu.w d5,d3 { mulitply with bigit from multiplier }
|
|
move.l d3,4(sp) { store into result }
|
|
|
|
move.l d4,d3
|
|
swap d3
|
|
mulu.w d5,d3
|
|
add.l d3,2(sp) { add to result }
|
|
|
|
swap d5 { [TOP 8 BITS SHOULD BE ZERO !] }
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|
|
|
move.w d4,d3
|
|
mulu.w d5,d3 { mulitply with bigit from multiplier }
|
|
add.l d3,2(sp) { store into result (no carry can occur here) }
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|
|
|
move.l d4,d3
|
|
swap d3
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|
mulu.w d5,d3
|
|
add.l d3,(sp) { add to result }
|
|
{ [TOP 16 BITS SHOULD BE ZERO !] }
|
|
movem.l 2(sp),d4-d5 { get the 48 valid mantissa bits }
|
|
clr.w d5 { (pad to 64) }
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|
|
|
move.l #$0000ffff,d3
|
|
@mlabel7:
|
|
cmp.l d3,d4 { multiply (shift) until }
|
|
bhi @mlabel8 { 1 in upper 16 result bits }
|
|
cmp.w #9,d0 { give up for denormalized numbers }
|
|
ble @mlabel8
|
|
swap d4 { (we''re getting here only when multiplying }
|
|
swap d5 { with a denormalized number; there''s an }
|
|
move.w d5,d4 { eventual loss of 4 bits in the rounding }
|
|
clr.w d5 { byte -- what a pity 8-) }
|
|
subq.w #8,d0 { decrement exponent }
|
|
subq.w #8,d0
|
|
bra @mlabel7
|
|
@mlabel8:
|
|
move.l d5,d1 { get rounding bits }
|
|
rol.l #8,d1
|
|
move.l d1,d3 { see if sticky bit should be set }
|
|
and.l #$ffffff00,d3
|
|
beq @mlabel9
|
|
or.b #1,d1 { set "sticky bit" if any low-order set }
|
|
@mlabel9:
|
|
addq.w #8,sp { remove accumulator from stack }
|
|
jmp SINGLE_NORM{ (result in d4) }
|
|
|
|
@mretz:
|
|
addq.w #8,sp { release accumulator space }
|
|
@mretzz:
|
|
moveq.l #0,d0 { save zero as result }
|
|
lsl.w #1,d2 { and set it sign as for d2 }
|
|
roxr.l #1,d0
|
|
movem.l (sp)+,d2-d5
|
|
rts { no normalizing neccessary }
|
|
end;
|
|
|
|
|
|
Procedure Single_Div;Assembler;
|
|
{--------------------------------------------}
|
|
{ Low-level routine to dividr two single }
|
|
{ IEEE floating point values. Never called }
|
|
{ directly. }
|
|
{ Om Entry: }
|
|
{ d1/d0 = u/v = operation to perform. }
|
|
{ On Exit: }
|
|
{ d0 = result. }
|
|
{ Registers destroyed: d0,d1 }
|
|
{ stack space used (and restored): 8 bytes. }
|
|
{--------------------------------------------}
|
|
ASM
|
|
XDEF SINGLE_DIV
|
|
{ u = d1 = dividend }
|
|
{ v = d0 = divisor }
|
|
tst.l d0 { check if divisor is 0 }
|
|
bne @dno_exception
|
|
|
|
move.l #$7f800000,d0
|
|
btst #31,d1 { transfer sign of dividend }
|
|
beq @dclear
|
|
bset #31,d0
|
|
@dclear:
|
|
rts
|
|
|
|
@dno_exception:
|
|
move.l d1,d4 { d4 = u, d5 = v }
|
|
move.l d0,d5
|
|
movem.l d2-d5,-(sp) { save registers }
|
|
|
|
move.l #$7fffff,d3
|
|
move.l d4,d0 { d0 = u.exp }
|
|
and.l d3,d4 { remove exponent from u.mantissa }
|
|
swap d0
|
|
move.w d0,d2 { d2 = u.sign }
|
|
|
|
move.l d5,d1 { d1 = v.exp }
|
|
and.l d3,d5 { remove exponent from v.mantissa }
|
|
swap d1
|
|
eor.w d1,d2 { d2 = u.sign ^ v.sign (in bit 15) }
|
|
|
|
moveq.l #15,d3
|
|
bclr d3,d0 { kill sign bit }
|
|
bclr d3,d1 { kill sign bit }
|
|
lsr.w #7,d0
|
|
lsr.w #7,d1
|
|
|
|
moveq.l #-1,d3
|
|
cmp.b d3,d0 { comparison with #0xff }
|
|
beq @dlabel1 { u == NaN ;; u== Inf }
|
|
cmp.b d3,d1
|
|
beq @dlabel2 { v == NaN ;; v == Inf }
|
|
tst.b d0
|
|
bne @dlabel4 { u not zero nor denorm }
|
|
tst.l d4
|
|
beq @dlabel3 { 0/ ? }
|
|
|
|
@dlabel4:
|
|
tst.w d1
|
|
bne @dnospec
|
|
|
|
tst.l d5
|
|
bne @dnospec
|
|
bra @dretinf { x/0 -> +/- Inf }
|
|
|
|
@dlabel1:
|
|
tst.l d4 { u == NaN ? }
|
|
bne @dretnan { NaN/ x }
|
|
cmp.b d3,d1
|
|
beq @dretnan { Inf/Inf or Inf/NaN }
|
|
{ bra dretinf ; Inf/x ; x != Inf && x != NaN }
|
|
{--------------------------------------------------------------------}
|
|
{ Return infinity with correct sign. }
|
|
{--------------------------------------------------------------------}
|
|
@dretinf:
|
|
move.l #$ff000000,d0
|
|
lsl.w #1,d2
|
|
roxr.l #1,d0 { shift in high bit as given by d2 }
|
|
@dreturn:
|
|
movem.l (sp)+,d2-d5
|
|
rts
|
|
|
|
@dlabel2:
|
|
tst.l d5
|
|
bne @dretnan { x/NaN }
|
|
{ bra dretzero ; x/Inf -> +/- 0 }
|
|
{--------------------------------------------------------------------}
|
|
{ Return correct signed zero. }
|
|
{--------------------------------------------------------------------}
|
|
@dretzero:
|
|
moveq.l #0,d0 { zero destination }
|
|
lsl.w #1,d2 { set X bit accordingly }
|
|
roxr.l #1,d0
|
|
bra @dreturn
|
|
|
|
@dlabel3:
|
|
tst.w d1
|
|
bne @dretzero { 0/x ->+/- 0 }
|
|
tst.l d4
|
|
bne @dretzero { 0/x }
|
|
{ bra dretnan 0/0 }
|
|
{--------------------------------------------------------------------}
|
|
{ Return NotANumber }
|
|
{--------------------------------------------------------------------}
|
|
@dretnan:
|
|
move.l d3,d0 { d3 contains 0xffffffff }
|
|
lsr.l #1,d0
|
|
bra @dreturn
|
|
{--------------------------------------------------------------------}
|
|
{ End of Special Handling }
|
|
{--------------------------------------------------------------------}
|
|
@dnospec:
|
|
moveq.l #23,d3
|
|
bset d3,d4 { restore implied leading "1" }
|
|
tst.w d0 { check for zero exponent - no leading "1" }
|
|
bne @dlabel5
|
|
bclr d3,d4 { remove it }
|
|
add.w #1,d0 { "normalize" exponent }
|
|
@dlabel5:
|
|
tst.l d4
|
|
beq @dretzero { dividing zero }
|
|
|
|
bset d3,d5 { restore implied leading "1" }
|
|
tst.w d1 { check for zero exponent - no leading "1"}
|
|
bne @dlabel6
|
|
bclr d3,d5 { remove it }
|
|
add.w #1,d1 { "normalize" exponent }
|
|
@dlabel6:
|
|
|
|
sub.w d1,d0 { subtract exponents, }
|
|
add.w #BIAS4-8+1,d0 { add bias back in, account for shift }
|
|
add.w #34,d0 { add loop offset, +2 for extra rounding bits}
|
|
{ for denormalized numbers (2 implied by dbra)}
|
|
move.w #27,d1 { bit number for "implied" pos (+4 for rounding)}
|
|
moveq.l #-1,d3 { zero quotient (for speed a one''s complement) }
|
|
sub.l d5,d4 { initial subtraction, u = u - v }
|
|
@dlabel7:
|
|
btst d1,d3 { divide until 1 in implied position }
|
|
beq @dlabel9
|
|
|
|
add.l d4,d4
|
|
bcs @dlabel8 { if carry is set, add, else subtract }
|
|
|
|
addx.l d3,d3 { shift quotient and set bit zero }
|
|
sub.l d5,d4 { subtract, u = u - v }
|
|
dbra d0,@dlabel7 { give up if result is denormalized }
|
|
bra @dlabel9
|
|
@dlabel8:
|
|
addx.l d3,d3 { shift quotient and clear bit zero }
|
|
add.l d5,d4 { add (restore), u = u + v }
|
|
dbra d0,@dlabel7 { give up if result is denormalized }
|
|
@dlabel9:
|
|
subq.w #2,d0 { remove rounding offset for denormalized nums }
|
|
not.l d3 { invert quotient to get it right }
|
|
|
|
clr.l d1 { zero rounding bits }
|
|
tst.l d4 { check for exact result }
|
|
beq @dlabel10
|
|
moveq.l #-1,d1 { prevent tie case }
|
|
@dlabel10:
|
|
move.l d3,d4 { save quotient mantissa }
|
|
jmp SINGLE_NORM{ (registers on stack removed by norm_sf) }
|
|
end;
|
|
|
|
|
|
Procedure Single_Cmp; Assembler;
|
|
{--------------------------------------------}
|
|
{ Low-level routine to compare single two }
|
|
{ single point values.. }
|
|
{ Never called directly. }
|
|
{ On Entry: }
|
|
{ d1 and d0 Values to compare }
|
|
{ d0 = first operand }
|
|
{ On Exit: }
|
|
{ Flags according to result }
|
|
{ Registers destroyed: d0,d1 }
|
|
{--------------------------------------------}
|
|
Asm
|
|
XDEF SINGLE_CMP
|
|
tst.l d0 { check sign bit }
|
|
bpl @cmplab1
|
|
neg.l d0 { negate }
|
|
bchg #31,d0 { toggle sign bit }
|
|
@cmplab1:
|
|
tst.l d1 { check sign bit }
|
|
bpl @cmplab2
|
|
neg.l d1 { negate }
|
|
bchg #31,d1 { toggle sign bit }
|
|
@cmplab2:
|
|
cmp.l d1,d0 { compare... }
|
|
rts
|
|
end;
|
|
|
|
|
|
|
|
Procedure LongMul;Assembler;
|
|
{--------------------------------------------}
|
|
{ Low-level routine to multiply two signed }
|
|
{ 32-bit values. Never called directly. }
|
|
{ On entry: d1,d0 = 32-bit signed values to }
|
|
{ multiply. }
|
|
{ On Exit: }
|
|
{ d0 = result. }
|
|
{ Registers destroyed: d0,d1 }
|
|
{ stack space used and restored: 10 bytes }
|
|
{--------------------------------------------}
|
|
Asm
|
|
XDEF LONGMUL
|
|
cmp.b #2,Test68000 { Are we on a 68020+ cpu }
|
|
blt @Lmulcontinue
|
|
muls.l d1,d0 { yes, then directly mul... }
|
|
rts { return... result in d0 }
|
|
@Lmulcontinue:
|
|
move.l d2,a0 { save registers }
|
|
move.l d3,a1
|
|
|
|
move.l d0,-(sp)
|
|
move.l d1,-(sp)
|
|
|
|
movem.w (sp)+,d0-d3 { u = d0-d1, v = d2-d3 }
|
|
|
|
move.w d0,-(sp) { sign flag }
|
|
bpl @LMul1 { is u negative ? }
|
|
neg.w d1 { yes, force it positive }
|
|
negx.w d0
|
|
@LMul1:
|
|
tst.w d2 { is v negative ? }
|
|
bpl @LMul2
|
|
neg.w d3 { yes, force it positive ... }
|
|
negx.w d2
|
|
not.w (sp) { ... and modify flag word }
|
|
@LMul2:
|
|
ext.l d0 { u.h <> 0 ? }
|
|
beq @LMul3
|
|
mulu.w d3,d0 { r = v.l * u.h }
|
|
@LMul3:
|
|
tst.w d2 { v.h <> 0 ? }
|
|
beq @LMul4
|
|
mulu.w d1,d2 { r += v.h * u.l }
|
|
add.w d2,d0
|
|
@LMul4:
|
|
swap d0
|
|
clr.w d0
|
|
mulu.w d3,d1 { r += v.l * u.l }
|
|
add.l d1,d0
|
|
move.l a1,d3
|
|
move.l a0,d2
|
|
tst.w (sp)+ { should the result be negated ? }
|
|
bpl @LMul5 { no, just return }
|
|
neg.l d0 { else r = -r }
|
|
@LMul5:
|
|
rts
|
|
end;
|
|
|
|
|
|
|
|
Procedure Long2Single;Assembler;
|
|
{--------------------------------------------}
|
|
{ Low-level routine to convert a longint }
|
|
{ to a single floating point value. }
|
|
{ On entry: d0 = longint value to convert. }
|
|
{ On Exit: }
|
|
{ d0 = single IEEE value }
|
|
{ Registers destroyed: d0,d1 }
|
|
{ stack space used and restored: 8 bytes }
|
|
{--------------------------------------------}
|
|
Asm
|
|
XDEF LONG2SINGLE
|
|
movem.l d2-d5,-(sp) { save registers to make norm_sf happy}
|
|
|
|
move.l d0,d4 { prepare result mantissa }
|
|
move.w #BIAS4+32-8,d0 { radix point after 32 bits }
|
|
move.l d4,d2 { set sign flag }
|
|
bge @l2slabel1 { nonnegative }
|
|
neg.l d4 { take absolute value }
|
|
@l2slabel1:
|
|
swap d2 { follow SINGLE_NORM conventions }
|
|
clr.w d1 { set rounding = 0 }
|
|
jmp SINGLE_NORM
|
|
end;
|
|
|
|
|
|
Procedure LongDiv; Assembler;
|
|
{--------------------------------------------}
|
|
{ Low-level routine to do signed long }
|
|
{ division. }
|
|
{ On entry: d0/d1 operation to perform }
|
|
{ On Exit: }
|
|
{ d0 = quotient }
|
|
{ d1 = remainder }
|
|
{ Registers destroyed: d0,d1,d6 }
|
|
{ stack space used and restored: 10 bytes }
|
|
{--------------------------------------------}
|
|
asm
|
|
XDEF LONGDIV
|
|
cmp.b #2,Test68000 { can we use divs ? }
|
|
blt @continue
|
|
tst.l d1
|
|
beq @zerodiv2
|
|
move.l d1,d6
|
|
clr.l d1 { clr }
|
|
tst.l d0 { check sign of d0 }
|
|
bpl @posdiv
|
|
move.l #$ffffffff,d1{ sign extend into d1 }
|
|
@posdiv:
|
|
divsl.l d6,d1:d0
|
|
rts
|
|
@continue:
|
|
|
|
move.l d2,a0 { save registers }
|
|
move.l d3,a1
|
|
move.l d4,-(sp) { divisor = d1 = d4 }
|
|
move.l d5,-(sp) { divident = d0 = d5 }
|
|
|
|
move.l d1,d4 { save divisor }
|
|
move.l d0,d5 { save dividend }
|
|
|
|
clr.w -(sp) { sign flag }
|
|
|
|
clr.l d0 { prepare result }
|
|
move.l d4,d2 { get divisor }
|
|
beq @zerodiv { divisor = 0 ? }
|
|
bpl @LDiv1 { divisor < 0 ? }
|
|
neg.l d2 { negate it }
|
|
not.w (sp) { remember sign }
|
|
@LDiv1:
|
|
move.l d5,d1 { get dividend }
|
|
bpl @LDiv2 { dividend < 0 ? }
|
|
neg.l d1 { negate it }
|
|
not.w (sp) { remember sign }
|
|
@LDiv2:
|
|
{;== case 1) divident < divisor}
|
|
cmp.l d2,d1 { is divident smaller then divisor ? }
|
|
bcs @LDiv7 { yes, return immediately }
|
|
{;== case 2) divisor has <= 16 significant bits}
|
|
tst.w d4
|
|
bne @LDiv3 { divisor has only 16 bits }
|
|
move.w d1,d3 { save dividend }
|
|
clr.w d1 { divide dvd.h by dvs }
|
|
swap d1
|
|
beq @LDiv4 { (no division necessary if dividend zero)}
|
|
divu d2,d1
|
|
@LDiv4:
|
|
move.w d1,d0 { save quotient.h }
|
|
swap d0
|
|
move.w d3,d1 { (d0.h = remainder of prev divu) }
|
|
divu d2,d1 { divide dvd.l by dvs }
|
|
move.w d1,d0 { save quotient.l }
|
|
clr.w d1 { get remainder }
|
|
swap d1
|
|
bra @LDiv7 { and return }
|
|
{;== case 3) divisor > 16 bits (corollary is dividend > 16 bits, see case 1)}
|
|
@LDiv3:
|
|
moveq.l #31,d3 { loop count }
|
|
@LDiv5:
|
|
add.l d1,d1 { shift divident ... }
|
|
addx.l d0,d0 { ... into d0 }
|
|
cmp.l d2,d0 { compare with divisor }
|
|
bcs @LDiv6
|
|
sub.l d2,d0 { big enough, subtract }
|
|
addq.w #1,d1 { and note bit into result }
|
|
@LDiv6:
|
|
dbra d3,@LDiv5
|
|
exg d0,d1 { put quotient and remainder in their registers}
|
|
@LDiv7:
|
|
tst.w d5 { must the remainder be corrected ? }
|
|
bpl @LDiv8
|
|
neg.l d1 { yes, apply sign }
|
|
{ the following line would be correct if modulus is defined as in algebra}
|
|
{; add.l sp@(6),d1 ; algebraic correction: modulus can only be >= 0}
|
|
@LDiv8:
|
|
tst.w (sp)+ { result should be negative ? }
|
|
bpl @LDiv9
|
|
neg.l d0 { yes, negate it }
|
|
@LDiv9:
|
|
move.l a1,d3
|
|
move.l a0,d2
|
|
move.l (sp)+,d5
|
|
move.l (sp)+,d4
|
|
rts { en exit : remainder = d1, quotient = d0 }
|
|
@zerodiv:
|
|
move.l a1,d3 { restore stack... }
|
|
move.l a0,d2
|
|
move.w (sp)+,d1 { remove sign word }
|
|
move.l (sp)+,d5
|
|
move.l (sp)+,d4
|
|
@zerodiv2:
|
|
move.l #200,d0
|
|
jsr HALT_ERROR { RunError(200) }
|
|
rts { this should never occur... }
|
|
end;
|
|
|
|
|
|
Procedure LongMod;Assembler;
|
|
{ see longdiv for info on calling convention }
|
|
asm
|
|
XDEF LONGMOD
|
|
jsr LONGDIV
|
|
move.l d1,d0 { return the remainder in d0 }
|
|
rts
|
|
end;
|
|
|
|
{
|
|
$Log$
|
|
Revision 1.1 1998-03-25 11:18:44 root
|
|
Initial revision
|
|
|
|
Revision 1.5 1998/01/26 12:01:47 michael
|
|
+ Added log at the end
|
|
|
|
|
|
|
|
Working file: rtl/m68k/lowmath.inc
|
|
description:
|
|
----------------------------
|
|
revision 1.4
|
|
date: 1998/01/05 00:33:30; author: carl; state: Exp; lines: +144 -156
|
|
* Several minor bugfixes
|
|
----------------------------
|
|
revision 1.3
|
|
date: 1997/12/14 19:03:36; author: carl; state: Exp; lines: +11 -12
|
|
+ uses now correct register conventions
|
|
----------------------------
|
|
revision 1.2
|
|
date: 1997/12/01 12:37:20; author: michael; state: Exp; lines: +14 -0
|
|
+ added copyright reference in header.
|
|
----------------------------
|
|
revision 1.1
|
|
date: 1997/11/27 13:55:47; author: carl; state: Exp;
|
|
Internal RTL math functions for m68k.
|
|
=============================================================================
|
|
}
|